Page:Proceedings of the Royal Society of London Vol 69.djvu/457

Rh these experiments have a wider application than to the cylinder experimented upon, Consider two similar homogeneous cylinders having the same magnetic properties and the same specific resistance, and let the ratio of their dimensions be n. As the magnetism pene- trates from the outside into the iron by a diffusion process, and a kinematic coefficient of diffusion is of two dimensions in space and one inversely in time, it follows that if the cylinders be each rotated in a magnetic field of the same intensity, then to induce the same electromotive force at similar points the speed of rotation must vary inversely as ?t' 2, and the induced currents will be similar in the two cylinders. In (Table I is given the periodic time or frequency at which similar electric and magnetic events will happen in similar cylinders of different diameters.

I. Madial Variation of Intensity of Magnetic Induction. Five different periodic times have been dealt with, namely, 360, 180, 90, 45, and 22 -5 seconds. The collected results for 360, 90, and 45 seconds are given in figs. 2, 4, 6 respectively, and have been taken from Table II which contains the complete data. The curves show approximately how the maximum intensity of induction varies at different depths of the cylinder, and have been obtained by first plotting the maximum average induction per sq. cm. for each coil 1, 2, 3 at its mean radius. We notice at once how marked is the effect of variation of frequency upon the distribution of induction. Moreover, for the smaller periodic times we notice how much more marked are the effects for intermediate values of the external magnetising force.

The maximum intensity of induction at the surface of the cylinder has been taken from curves, and in each case the corresponding value at the centre has been expressed as a percentage of it. Fig. 7 gives the results so obtained plotted in terms of the maximum intensity of induction at the surface. The curves are numbered 360, 180, 90, 45, 22'5 to correspond with the periodic time in each case. AVe see that as the frequency is increased the centre is more shielded ; moreover with increase of frequency the range over which the interior of the cylinder is shielded is increased. At 45 seconds periodic time the surface value of the intensity of magnetic induction at which the effects of induced currents begin to rapidly diminish is about 16,000. At 90 seconds it is about 11,000, but the rate is slower. At 180 seconds the change starts at about 7000 and is more gradual. At 360 seconds the dis- turbing effects due to induced currents are probably small. The distribution of intensity of induction when the cylinder is not rota- ting is not known, and probably varies with the intensity of magnetic force. The curves in fig. 2 may perhaps be trusted to give some indi- cation of the distribution if the cylinder was not rotating. The dotted curve in fig. 2, giving B 15,400 at the centre of the cylinder, probably gives this value too low, owing to some unknown error. The curve is